31.19 - Summary
Reflection occurs when light bounces back from a surface, rather than passing
through it or being absorbed. Reflection causes objects to be visible.
In optics, it is often useful to represent the path of light in the form of a light ray, a
straight line that can be used to determine how light is affected by mirrors and
lenses.
Planar mirrors are the simplest and most common type of mirror. In a planar mirror,
your image has the same dimensions as you do and it appears to be the same
distance behind the mirror as you are in front of it. The image is reversed front to
back, but not right to left or top to bottom.
When you see your image in a planar mirror, you are seeing a virtual image, so
called because you cannot project this image onto a screen at its perceived
location. A virtual image appears to be on the opposite side of a mirror from the
object it is created from, and its image distance is negative.
In contrast, a real imagecan be projected onto a screen, and it occurs on the same
side of a mirror as the object it is created from. Its image distance is positive.
Curved mirrors can create virtual or real images.
The law of reflection states that for a light ray reflecting off a mirror, the angle of
incidence equals the angle of reflection. These two angles are measured between
the light ray and a line normal to the surface of the mirror.
A ray diagram can help you determine the location of the image an object casts in a
planar mirror. Draw two incident rays from any point on the object to the mirror.
Draw the reflected rays using the law of reflection, and trace their virtual extensions
backward behind the mirror as dashed lines. The point of the image corresponding
to the point source of the incident rays on the object is located where these virtual
rays intersect.
Spherical mirrors have a constant curvature. A mirror is called concave if it curves toward (around) the object it reflects. A convex mirror curves
away from the object it reflects.
All points on a spherical mirror are equidistant from its center of curvature. The principal axis is a line through the center of curvature and the
midpoint of the mirror. Paraxial rays are incident rays close to the principal axis of a mirror. The reflections of these rays converge at the focal
point if the rays are parallel to the principal axis. The height of an image is negative if the image is inverted.
The focal length of a curved mirror is the distance between a mirror and its focal point. By convention, it is positive for a concave mirror where
the focal point is on the same side of the mirror as the object. It is negative for a convex mirror where the focal point is on the opposite side.
Spherical mirrors exhibit spherical aberration because only paraxial incident rays converge at the focal point. With a parabolic mirror, all
incident rays that are parallel to the principal axis converge at the focal point.
Ray tracing for concave and convex mirrors is more complicated than for planar mirrors, but it can help you determine the orientation, relative
size, and location (or type) of an image.
The mirror equation relates the distances of an object and its image from a mirror to the focal length of the mirror. The magnification equations
define the magnification of an image created by a mirror. If the magnification is known, we may calculate the image height from the object
height or the image distance from the object distance, or vice versa.
Law of reflectionși = șr
Focal length of concave mirrorf = r/2
Focal length of convex mirrorf = –r/2
Mirror equationMagnification equations